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ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

A Novel Optimum Technique for JPEG 2000 
Post Compression Rate Distortion Algorithm 

Shaik.Mahaboob Basha 1 , Dr. B.C.Jinaga 2 
1 Department of Electronics and Communication Engineering, Priyadarshini College of Engineering and Technology, 

Nellore, India 


2 Retired Professor, Department of Electronics and Communication Engineering, J. N.T. University, Hyderabad, India 


Abstract — The new technique we proposed in this paper based 
on Hidden Markov Model in the field of post compression rate 
distortion algorithms certainly meet the requirements of high 
quality still images. The existing technology has been 
extensively applied in modern image processing. Development 
of image compression algorithms is becoming increasingly 
important for obtaining a more informative image from several 
source images captured by different modes of imaging systems 
or multiple sensors. The JPEG 2000 image compression 
standard is very sensitive to errors. The JPEG2000 system 
provides scalability with respect to quality, resolution and 
color component in the transfer of images. But some of the 
applications need certainly qualitative images at the output 
ends. In our architecture the Proto-object also introduced as 
the input ant bit rate allocation and rate distortion has been 
discussed for the output image with high resolution. In this 
paper, we have also discussed our novel response dependent 
condensation image compression which has given scope to go 
for this post compression Rate Distortion Algorithm (PCRD) 
of JPEG 2000 standard. This proposed technique outperforms 
the existing methods in terms of increasing efficiency, 
optimum PSNR values at different bpp levels. The proposed 
technique involves Hidden Markov Model to meet the 
requirements for higher scalability and also to increase the 
memory storage capacity. 

Index Terms— JPEG 2000, Hidden Markov Model, Rate 
distortion, Scalability, Image compression, post compression 

I. Introduction 

JPEG 2000 is a new digital imaging system that builds on 
JPEG but differs from it. It utilizes a Wavelet transform and an 
arithmetic coding scheme to achieve scalability in its design 
and operation. It offers improved compression, better quality 
for a given file size under most circumstances. This is 
especially true at very high compression. As a result a greater 
emphasis is being placed on the design of new and efficient 
image coders for voice communication and transmission. 
Today applications of image coding and compression have 
become very numerous. Many applications involve the real 
time coding of image signals, for use in mobile satellite 
communications, cellular telephony, and audio for 
videophones or video teleconferencing systems. The recently 
developed Post compression Rate Distortion Algorithms for 
JPEG 2000 standard 2000 standard, which incorporates 
wavelet at the core of their technique, provides many excellent 
features compared to the other algorithms. From the time 
David Taubman introduced Post compression Rate Distortion 

©2011 ACEEE 

Algorithms for JPEG 2000 in terms of scalability, many 
algorithms have been forced into various fields of applications. 
The Discrete Wavelet Transform coding (DWT) is the widely 
used transform technique in JPEG 2000 applications. The 
applications require some improvements in scalability, 
efficiency, memory storage capacity.So; we proposed Hidden 
Markov Model technique in this paper to JPEG 2000 still image 
compression standard. The outline of the paper is as follows. 
Section II about the background of the proposed technique 
which involves overview of JPEG 2000 and Response 
Dependent Condensation Image Compression Algorithm. 
Section III describes about the Methodology of the 
architecture. Section IV gives simulation results of our work. 
Conclusion appears in Section V. 


A. Overview ofJPEG2000 

The JPEG 2000 has Superior low bit-rate performance at 
all bit rates was considered desirable, improved performance 
at low bit-rates, with respect to JPEG was considered to be 
an important requirement for JPEG2000. Seamless compression 
of image components each from 1 to 16 bits deep, was desired 
from one unified compression architecture. Progressive 
transmission is highly desirable when receiving imagery over 
slow communication links. Code-stream organizations which 
are progressive by pixel accuracy and quality improve the 
quality of decoded imagery as more data are received. Code- 
stream organizations which are progressive by "resolution" 
increase the resolution, or size, of the decoded imagery as 
more data are received. [19]. Both lossless and lossy 
compression was desired, again from single compression 
architecture. It was desired to achieve lossless compression 
in the natural course of progressive decoding. JPEG 2000 is 
also having other salient features such as code stream 
accessing random manner, processing, robustness to bit- 
errors and sequential build-up capability. Due to this the JPEG 
2000 is having the quality to allow for encoding of an image 
from top to bottom in a sequential fashion without the need 
to buffer in an entire image. This is very useful for low memory 
implementations in scan-based systems. [19] In the 
JPEG2000 core coding system, the sample data 
transformations, sample data coding, rate-distortion 
optimization, and code stream reorganization. The first sample 
data transformations stage compacts the energy of the image 
through the Discrete Wavelet Transform (DWT), and sets 



ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

the range of image samples. Then, the image is logically 
partitioned into code locks that are independently coded by 
the sample data coding stage, also called Tier- 1 . [21] 

B. Response Dependent Condensation Algorithm 

Our Response Dependent Condensation Image 
Compression Algorithm is to develop an array error packing 
addressing methodology from original image and error image 
and it depends on the application. The compression ratios of 
different transforms have observed. To calculate compression 
ratio, a 2-dimensional 8X8 image was considered. First image 
is converted into binary format then it is processed. The 
output is also binary format and it is given to MATLAB to 
reconstruct the output. The simulation results using the 
hybrid transform has given better results compared to other 
transformation techniques(DCT-Discrete Cosine Transform, 
DFT- Discrete Fourier Transform, DST-Discrete Sine 
Transform, DWT- Discrete Walsh Transform, DHT- Discrete 
Hartley Transform). Wavelet analysis is capable of revealing 
aspects of data that other signal analysis techniques such as 
Fourier analysis miss aspects like trends, breakdown points, 
discontinuities in higher derivatives, and self-similarity [22] 
The component transform provides de-correlation among 
image components (R, G, and B). This improves the 
compression and allows for visually relevant quantization. 
When the reversible path is used, the Reversible Component 
Transform (RCT) is used, which maps integers to integers. 
When the irreversible path is used the YCbCr transform is 
used as is common with the original JPEG 2000. [22] The 
dynamic condensation matrix is response dependent and the 
corresponding condensation is referred as Response- 
Dependent Condensation. The dynamic condensation matrix 
is defined as the relations of an eigenvector between the 
input and output. This novel approach of studying linear 
effects in JPEG 2000 compression of color images. The DCT 
has been performed on the bench mark figures and each 
element in each block of the image is then quantized using a 
quantization matrix of quality level 50. At this point many of 
the elements become zeroed out, and the images takes up 
much less space to store. The image can now be 
decompressed using proposed algorithm. At quality level 50 
there is almost no visible loss in this image, but there is high 
compression. At lower quality levels, the quality goes down 
by a lot, but the compression does not increase very much. 
Similarly, experiments are also conducted to various images 
to find out the compression. The Response Dependent 
Compression Algorithm is applied to calculate the image 
compression. It can be observed that noise is slightly 
removed but there is a huge change in image dimensions. 
Response Dependent Compression Algorithm is applied to 
calculate the image compression. It can be observed that 
noise is slightly removed but there is a huge change in image 
dimensions. This response dependent condensation 
algorithm gives better results compared to other 
transformation techniques. Our algorithm which discussed 
about the gives an idea and scope to move further for proto- 
object segmentation with reference to the scalability by 
replacing the basic Discrete Wavelet Transform(DWT) with 

©2011 ACEEE 

other waveform techniques including present technique 
Hidden Markov Model (HMM) for certain applications 
involving still images. 


A Hidden Markov Model 

Hidden Markov Model (HMM)is the technique we are 
using in our proposed work as it is best suitable for image 
processing techniques mainly segmentation and 
compression. The standard formula for estimating the model 
according to the rate distortion and bit rate allocation can be 
derived from our architecture To segment an image, the bit 
rate allocation that is in terms of pixel to pixels of the Proto- 
image we are giving as the input image handled easily with 
HMM. The problems in our work can be handled by HMM 
as it is suitable for smoothing and statistical significance. 
The probability that a sequence drawn from some null 
distribution will have an HMM probability in the case of the 
forward algorithm or a maximum state sequence probability 
at least as large as that of a particular output sequence. If a 
HMM is used to evaluate the relevance of a hypothesis for a 
particular output sequence, [25] the statistical significance 
indicates the false positive rate associated with accepting 
the hypothesis for the output sequence. 

Figure 1 .Architecture of Hidden Markov Model 

The task is to compute, given the parameters of the model 
and a particular output sequence up to time t, the probability 
distribution over hidden states for a point in time in the past. 
To compute the forward -backward algorithm is an efficient 
method for computing the smoothed values for all hidden 
state variables and Hidden Markov Model can represent even 

P{x{k)\y{\)....,y{t)) f0lk< L __. (1) 

more complex behavior when the output of the states is rep- 
resented as mixture of two or more Gaussians, in which case 
the probability of generating an observation is the product of 
the probability of first selecting one of the Gaussians and the 
probability of generating that observation from that Gaussian. 
This is the reason for choosing the Hidden Markov Model 
for our proposed work. The proposed architecture block 
diagram of our work is described in this section as follows.The 
block diagram of our proposed architecture with reference to 
the paper mentioned in [23]. 

B. Scalability 

The high buffering cost of embedded compression is 
unavoidable so long as we insist on generating the embedded 
bit-stream in order. An alternate approach, however, is to 
process the image or sub band samples locally while 



ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

producing the embedded bit-steam prior to a final 
reorganization step can be significantly smaller than the image 
itself, assuming that compression is achieved for 
constructing embedded bit-streams[19] 

C. PCRD Coding and Pre-coding stages 

According to the general derived PCRD algorithm of 
David Taubman and Marcellin describes algorithm which 
may be used to optimize the set of code -block truncation 
points, {z }, so as to minimize the overall distortion, D, subject 
to an overall length constraint, L .The same algorithm may 
be used to minimize the overall length subject to a distortion 
constraint if desired. We refer to this optimization strategy 
as post-compression rate-distortion optimization (PCRD-opt). 
The algorithm is implemented by the compressor, which is 
expected to computer or estimate length and distortion 
contributions, L (z) and D <z) , for each truncation point, z = 
o,l,...., Z. Tis information will not normally be explicitly 
included in the pack-stream. As a result, the algorithm is not 
easily reapplied to a previously constructed pack-stream.. 
as a result, the algorithm is not easily reapplied to a previously 
constructed pack-stream may contain many quality layers. 
[19] Input image into PO regions and BG regions, and then 
reconsider both the construction of an operational RD curve 
in the coding pipeline and the implementation of an efficient 
rate control scheme in terms of PO regions. By using PO 
region segmentation instead of tile partition, defining the 
quality layer in terms of PO regions. 
By assuming overall distortion is additive 

r> = 

/>.(»i * 


It is desired to find the optimal selection of bit stream 
truncation points n t 'such that the overall distortion metric is 
minimized subject to a constraint. [24] 










Figure. 2. Blockdiagram of the Proposed Architecture 

R T 

> r = Y1 /*.■<»■>■ 


These are reflected in the partition system and coding pipe- 
line of the JPEG2000 system. [23] In the coding stage the op- 
erational RD curve is constructed in two steps: 1) the Tier-1 
output code-stream segments with a set of truncation points 

©2011 ACEEE 

for coding passes. The code-stream segment is the smallest 
unit for constructing the operational RD curve. 2) Quality 
layers of PO regions are developed in Tier-2, and this forms 
the final operational curve for the further purpose of rate 
control. [23] . Similarly in the post-coding stage, by using the 
actual RD functions of all the compressed data, the optimal 
truncation techniques attain the minimum image distortion 
for a given bit rate. Our rate control scheme is based on the 
estimation of RD slopes of the coding passes. Using these 
estimations, the selection of coding passes to yield a target 
bit rate can be performed without information related to the 
encoding process, or distortion measures based on the origi- 
nal image. [23] . The Quality scalability is achieved by divid- 
ing the wavelet transformed image into code-blocks. After 
that each code-block is encoded, a post-processing opera- 
tion determines the each code -block's embedded stream 
should be truncated in order to achieve a pre-defined bit-rate 
or distortion bound for the whole image. This bit-stream re- 
scheduling module is referred to as the Tier 2. It establishes 
a multi-layered representation of the final bit-stream, guaran- 
teeing an optimal performance at several bit rates or resolu- 
tions. [24] 

D. EBCOT Block 

The coding and ordering techniques adopted by 
JPEG2000 are based on the concept of Embedded Block 
Coding with Optimal Truncation (EBCOT), which is the 
subject of this chapter. Each sub band is partitioned into 
relatively small blocks). Division of sub bands into code- 
blocks, having the same dimensions in every subband. All 
sub bands are depicted with the size and the code -blocks 
appear to have different sizes of code-blocks. Each code- 
black, B is coded independently, producing an elementary 
embedded bit-stream, C Although any prefix of length, L 
should represent an efficient compression of the block's 
samples at the corresponding rate. 

E. Quantization 

The trade-off between rate and distortion is obtained by 
quantization. Wavelet coefficients can be divided by a 
different value for each sub-band. Alternatively, portions of 
the coded data can be discarded. This discarding of data can 
be done in a variety of creative ways. The proposed technique 
was implemented on several bench mark figures like Lena, 
River, House, Animal, River and also several sample figures 
including color and black/white images and observed that 
the results we got are comparably better. 

Fig.3.USID benchmark (Lena) 



ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

Table I. bpp versus computation times 

Fig.4.USID benchmark (Animal) 

Fig.5.USID benchmark (River) 

Fig.6.USID benchmark (House) 


The MATLAB used as the simulation tool to prove the 
better results on the bench mark figures such as Lena, River, 
House , Animal , River and also several sample figures 
including color and black and white images to the existing 



time (s) 
















■ , i 1 

"_ ^m^"" - r 

■ . ■__ _-t"I-/_"^ 

/\f i i 

3. __//__' ' 

i S 

1 i 1 

I 1 : 

Figure 8. Comparison of performance 
Table II. bpp versus psnr 



PSNR. (dB) 
















Figure 7. Comparison of bpp Vs time 

Figure 9. Comparison of bpp versus PSNR 

The experimental values from the tables I, II and III clearly 
shows that the new technique proposed in this paper has 
better values with respect to computation times, PSNR values 
at various bpp values. The complexity has been reduced by 
applying Hidden Markov Model in place of the other wavelet 

©2011 ACEEE 



ACEEE Int. J. on Information Technology, Vol. 01, No. 02, Sep 201 1 

transforms like DWT. In the post compression process the 
rate distortion and bit rate allocation will generally play a 
major role in various application requirements. This technique 
can also utilized to perform the object region coding and 
segmentation processing of different types of application 
images for different applications. 




PSNR (dB) 
















This is for the mobile, remote sensing, still image compression 
related applications. The JPEG image compression systems 
can be affected by soft errors because of their wide uses in 
remote sensing and medical imaging. In such applications, 
fault tolerance techniques are very important in detecting 
computer induced errors within the JPEG compression 
system, thus guaranteeing the quality of image output while 
employing the compression data format of the standard. Fault 
tolerance is different from error resilience in compression 
standards. Resilience generally refers to the capabilities of 
recovering from errors introduced by the transmission path 
of compressed data while fault tolerance protects against 
errors that are introduced by the computing resources 
executing the compressing and decompressing algorithms. 
Scalability is an important concept of JPEG2000 still image 
compression standard. The JPEG2000 codec is transform 
based, and resolution scalability is a direct consequence of 
the multi-resolution properties of the Discrete Wavelet 
Transform (DWT). A code stream is said to be resolution 
scalable if it contains identifiable subsets that represent 
successively lower resolution versions of the original image. 
Since bi-level images are invariably digitized at high 
resolutions, this property of the code-stream is potentially 
very useful. Consider the case where high resolution images 
are being viewed by a user over a network. Typically, the 
image at full resolution will be too large to display on the 
user's monitor. By making use of the inherent scalability of 
the JPEG2000 code stream, it is possible to stream only the 
relevant portions of the image to the client. This allows 
JPEG2000 content to be delivered in a manner which matches 
the user's display resolution. [26] [27] In JPEG2000, both the 
reversible and irreversible transforms can be implemented 
using a common lifting framework. In a broad sense, lifting 
provides a means to generate invertible mappings between 
sequences of numbers, and the invertibility is unaffected 
even when arbitrary operators, which may be linear or non- 
linear, are introduced in the lifting steps [26] [27] .This flexibility 
allows the use of non-linear rounding operations in the lifting 
steps, in order to ensure that the transform coefficients are 

©2011 ACEEE 

integers. In this paper we have discussed about the necessity 
of enhanced scalability for various applications. For better 
results the images were tested for different resolutions like5 1 2x5 1 2, 
256 x256. 


This paper proposes new technique in the field of Post 
compression Rate Distortion Algorithms for JPEG 2000 with 
Hidden Markov Model technique which outperforms the other 
existing methods in terms of scalability. It also showed better 
results in PSNR versus bpp and the computational complexity 
has been reduced considerably which increases the 
efficiency and memory storage capacity. 


The first author would like to thank Dr.I.Gopal Reddy- 
Director, Dr.O.Mahesh-Principal and the management 
committee of Priyadarshini College of Engineering & 
Technology, Nellore for their encouragement in doing this 
work and also very grateful to the different authors cited in 
the references. 


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©2011 ACEEE